Republicans are in turmoil, split between diehard conservatives and pragmatists in a battle for the soul and control of a party reeling from unexpected election setbacks last month.

The struggle is evident across the landscape. On Capitol Hill, Republicans are at odds over strategy and substance as they confront the “fiscal cliff” and a leader asserting his power over wayward members. Among voters, polls warn that Americans would blame Republicans if economic chaos ensues, while conservative interest groups insist this is no time to compromise. And among GOP insiders, a brawl could be looming over who chairs the party.

The schism is being aggravated almost daily in Congress, where the two factions are waging a fierce fight over how to deal with the budget crisis. House of Representatives Speaker John Boehner, R-Ohio, a veteran pragmatist whose instincts for compromise had been thwarted by the rise of the diehard conservatives, is his old self, offering deals and punishing those who defy him. The diehards are swinging back hard, publicly questioning Boehner’s leadership and offering reminders that they still have considerable financial and political muscle.

Republicans perceived as disloyal to Boehner are being punished. Four have been kicked off committees, and the diehards are angry.

“When one comes here and votes his conscience, and it’s not antithetical to the Republican platform, why should he suffer for it?” asked Rep. Trent Franks of Arizona. “The Republican cause, and the cause of freedom, is diminished.”

The rupture is a preview of things to come as the party begins charting a highly uncertain future.

Republicans were jolted on Election Day by losses few anticipated. Not only did President Barack Obama crush Republican Mitt Romney in the electoral vote count, but the party lost seats in the Senate and the House of Representatives.

The party leadership is far from secure. Former Rep. J.C. Watts, once the House’s highest-ranking black Republican, is being mentioned by some insiders as a possible challenger to Republican National Committee Chairman Reince Priebus when he seeks another term next month.

Republicans know that voters had delivered a strong message, one more difficult for party stalwarts to accept. Obama and fellow Democrats won with a pledge to raise taxes on the wealthy, a position virtually all Republicans ruled out.

Pragmatists have been slowly moving in a more conciliatory direction. Day after day, it seems, a previously unshakable Republican suggests he could accept some higher rates. The latest was Sen. Tom Coburn of Oklahoma, long regarded as a no-tax-increase hardliner.

At the same time, Boehner has defied the hardcore conservatives. He and his leadership team Monday offered a deficit reduction package that included $800 billion in new revenue; the diehards oppose any new revenue. They booted the four Republicans off committees, and Boehner allies have been warning colleagues privately that more such punishment could be forthcoming.

Two of the booted lawmakers spoke out at a Heritage Foundation forum this week. Rep. Justin Amish of Michigan said Boehner’s move was “a slap in the face to all young people who are thinking of becoming Republican.” The action was a signal that “dissent will not be tolerated,” added Rep. Tim Huelskamp of Kansas.

In the budget fight, polls suggest voters would blame Republicans if there’s no deal.

At the same time, conservative groups argue that unless Republicans stick to long-held fiscal principles, the party will stand for nothing – and, they warned, could face an uprising in 2014.

“You are entering a period of testing,” said a letter to congressional Republicans signed by about 100 conservative leaders. “The whole leftist apparatus is gearing up to panic you and to force you to cave in. Don’t do it.”

After the committee assignment drama, the Club for Growth, which donates to the campaigns of conservative Republicans, issued a new warning. It “stands ready to make sure that Republican primary voters are also watching the voting patterns of the big government crowd in the House GOP,” said Chris Chocola, president of the group.

But the pragmatists, generally veteran conservatives or those from swing districts, are well aware of the poll numbers, and they have been sending strong messages that they’re ready for compromise.

They would not dismiss the Boehner offer. “You’re going to have dissenters, but at the end of the day, this offer is better than no offer,” said Rep. Dennis Ross of Florida.

If there’s a trend developing, it’s probably on the side of conciliation. Some of the most conservative voices are talking in gentler tones.

Rep. James Lankford of Oklahoma makes it clear that he’s adamantly against higher taxes, noting that if taxes on dividends go up, it’ll be seniors and pension plans that will be particularly hurt. And he wants to know more about the negotiations.

“We’re mostly concerned that no one can see in the cockpit,” he said.

But he won’t go that extra step and criticize Boehner or the leadership.